A problem in mathematics is given to 3 students whose chances of solving it are 1/2, 1/3, 1/4.

Question

A problem in mathematics is given to 3 students whose chances of solving it are \(\frac{1}{2},\frac{1}{3},\frac{1}{4}.\) What is the probability that the 

(i) problem is solved? 

(ii) exactly one of them will solve it?

Answer 1

(i) Let A, B, C be the respective events of solving the problem. Then P(A) = \(\frac{1}{2}\), P(B) = \(\frac{1}{3}\) and P(C) = \(\frac{1}{4}\). Clearly A, B, C are independent events and the problem is solved if at least one student solves it.